Fluid models of gas discharges require the input of transport coefficients and rate coefficients that depend on the electron energy distribution function. Such coefficients are usually calculated from collision cross-section data by solving the electron Boltzmann equation (BE). In this paper we present a new user-friendly BE solver developed especially for this purpose, freely available under the name BOLSIG+, which is more general and easier to use than most other BE solvers available. The solver provides steady-state solutions of the BE for electrons in a uniform electric field, using the classical two-term expansion, and is able to account for different growth models, quasi-stationary and oscillating fields, electron–neutral collisions and electron–electron collisions. We show that for the approximations we use, the BE takes the form of a convection-diffusion continuity-equation with a non-local source term in energy space. To solve this equation we use an exponential scheme commonly used for convection-diffusion problems. The calculated electron transport coefficients and rate coefficients are defined so as to ensure maximum consistency with the fluid equations. We discuss how these coefficients are best used in fluid models and illustrate the influence of some essential parameters and approximations.

https://www3.nd.edu/~sst/teaching/AME60637/reading/2005_PSST_Hagelaar_Pitchford_bolsig.pdf

Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models

This paper presents theoretical calculations of the large-signal admittance and efficiency achievable in a silicon p-n-v-ns Read IMPATT diode. A simplified theory is employed to obtain a starting design. This design is then modified to achieve higher efficiency operation as specific device limitations are reached in large-signal (computer) operation. Self-consistent numerical solutions are obtained for equations describing carrier transport, carrier generation, and space-charge balance. The solutions describe the evolution in time of the diode and its associated resonant circuit. Detailed solutions are presented of the hole and electron concentrations, electric field, and terminal current and voltage at various points in time during a cycle of oscillation. Large-signal values of the diode's negative conductance, susceptance, average voltage, and power-generating efficiency are presented as a function of oscillation amplitude for a fixed average current density. For the structure studied, the largest microwave power-generating efficiency (18 percent at 9.6 GHz) has been obtained at a current density of 200 A/cm2, but efficiencies near 10 percent were obtained over a range of current density from 100 to 1000 A/cm2.

Large-signal analysis of a silicon Read diode oscillator

We have developed a numerical device model that consistently describes the current-voltage characteristics of polymer:fullerene bulk heterojunction solar cells. Bimolecular recombination and a temperature- and field-dependent generation mechanism of free charges are incorporated. It is demonstrated that in poly[2-methoxy-5-(3('),7(')-dimethyloctyloxy)-p-phenylene vinylene]- (OC1C10-PPV-) and [6,6]-phenyl C-61-butyric acid methyl ester- (PCBM-) (1:4 wt. %) based solar cells space-charge effects only play a minor role, leading to a relatively constant electric field in the device. Furthermore, at short-circuit conditions only 7% of all free carriers are lost due to bimolecular recombination. The model predicts that an increased hole mobility together with a reduction of the acceptor strength of 0.5 eV will lead to a maximum attainable efficiency of 5.5% in the PPV/PCBM-based solar cells.

Device model for the operation of polymer/fullerene bulk heterojunction solar cells

A three-dimensional (3-D) "atomistic" simulation study of random dopant induced threshold voltage lowering and fluctuations in sub-0.1 /spl mu/m MOSFETs is presented. For the first time a systematic analysis of random dopant effects down to an individual dopant level was carried out in 3-D on a scale sufficient to provide quantitative statistical predictions. Efficient algorithms based on a single multigrid solution of the Poisson equation followed by the solution of a simplified current continuity equation are used in the simulations. The effects of various MOSFET design parameters, including the channel length and width, oxide thickness and channel doping, on the threshold voltage lowering and fluctuations are studied using typical samples of 200 atomistically different MOSFETs. The atomistic results for the threshold voltage fluctuations were compared with two analytical models based on dopant number fluctuations. Although the analytical models predict the general trends in the threshold voltage fluctuations, they fail to describe quantitatively the magnitude of the fluctuations. The distribution of the atomistically calculated threshold voltage and its correlation with the number of dopants in the channel of the MOSFETs was analyzed based on a sample of 2500 microscopically different devices. The detailed analysis shows that the threshold voltage fluctuations are determined not only by the fluctuation in the dopant number, but also in the dopant position.

/pdf/random-dopant-induced-threshold-voltage-lowering-and-56qhk9ysdh.pdf

Random dopant induced threshold voltage lowering and fluctuations in sub-0.1 /spl mu/m MOSFET's: A 3-D "atomistic" simulation study

The avalanche region of an IMPATT (IMPact ionization Avalanche Transit Time) diode under small signal conditions is characterized by the fraction of the total alternating current that is carried by holes and electrons in their respective drift spaces and by a residual impedance. The current fractions are roughly in phase with the total current below, and nearly 180° out of phase above a resonance frequency that is proportional to the square root of direct current density. This paper extends the calculations of Gilden and Hines for the current fraction to include phase shifts in the avalanche region so that extended avalanche regions can be considered. Realistic values (α ≠ β in Si) for the ionization coefficients are used. Results of detailed numerical calculations for the current fractions as a function of frequency and direct current density are presented. For typical frequencies and current densities, the residual impedance is negligible and hole and electron current fractions are equal. The avalanche region at a given frequency and current density is then characterized by one complex number and the admittance of a diode containing the avalanche region and adjacent drift regions is easily calculated. Plots showing the admittance as a function of frequency and current density for typical structures are given. It is found that an optimal exponential growth rate of oscillations is obtained when the current density is such that the resonance frequency is about equal to one half the reciprocal transit time through the longest drift region. If the assumption is made that conditions giving the largest small-signal exponential growth rate give the best large-signal performance, an optimum Read-diode design is obtained for which the avalanche region width is a substantial fraction (≍ 1/3) of the drift region width.

Avalanche region of impatt diodes

Advances in LSI technology are beginning to outstrip architectural innovations and their implementation, calling for greater software productivity and development of better design aids.

The Use of LSI Modules in Computer Structures: Trends and Limitations

Measured dependence of lifetime upon local defect density and temperature in depletion layers of epitaxial silicon diodes

A unified approach to the solution of semiconductor boundary value problems is presented. The terminal voltage (including bulk drops) is derived by taking the total current as the independent variable. At semiconductor interfaces relationships between potential drops and carrier concentrations in the neutral regions are reviewed in terms of both the electrostatic and electrochemical potentials. The terminal voltage is expressed in terms of either the electrostatic or electrochemical potentials. Examples are presented to illustrate the techniques presented in this paper in terms of the familiar RP+NR and not so familiar RvNR diodes.

D.L. Scharfetter

Papers

Large-signal analysis of a silicon Read diode oscillator

Avalanche region of impatt diodes

The Use of LSI Modules in Computer Structures: Trends and Limitations

Measured dependence of lifetime upon local defect density and temperature in depletion layers of epitaxial silicon diodes

A unified treatment of semiconductor boundary value problems